A control device of a vehicle oil supply device has hitherto been known that includes an electric oil pump and a mechanical oil pump driven by an engine to supply oil to an oil supply destination. For example, this corresponds to an electric oil pump driving control device of a vehicle described in Patent Document 1. The vehicle described in Patent Document 1 provides idling reduction control for temporarily automatically stopping the engine in association with a stop of running of the vehicle. Since the mechanical oil pump is stopped as the engine stops during the idling reduction control, the electric oil pump driving control device drives the electric oil pump so as to supply oil to an automatic transmission etc. When the idling reduction control is canceled, the electric oil pump driving control device stops the electric oil pump if an engine rotation speed becomes equal to or greater than a predetermined rotation speed.